Computed tomography (CT) systems and methods are widely used, particularly for medical imaging and diagnosis. CT systems generally create images of one or more sectional slices through a subject's body. A radiation source, such as an X-ray source, irradiates the body from one side. At least one detector on the opposite side of the body receives radiation transmitted through the body. The attenuation of the radiation that has passed through the body is measured by processing electrical signals received from the detector.
A CT sinogram indicates attenuation through the body as a function of position along a detector array and as a function of the projection angle between the X-ray source and the detector array for various projection measurements. In a sinogram, the spatial dimensions refer to the position along the array of X-ray detectors. The time/angle dimension refers to the projection angle of X-rays, which changes as a function of time during a CT scan. The attenuation resulting from a portion of the imaged object (e.g., a vertebra) will trace out a sine wave around the vertical axis. Those portions farther from the axis of rotation correspond to sine waves with larger amplitudes, and the phase of the sine waves correspond to the angular positions of objects around the rotation axis. Performing an inverse Radon transform—or any other image reconstruction method—reconstructs an image from the projection data in the sinogram.
X-ray CT has found extensive clinical applications in cancer, heart, and brain imaging. As CT has been increasingly used for a variety of applications including, e.g., cancer screening and pediatric imaging, there has arisen a push to reduce the radiation dose of clinical CT scans to become as low as reasonably achievable. However, one challenge of reducing the radiation dose is that, as the measured intensity approaches the baseline level, noise can be on the same order of magnitude as the signal. When this occurs, baseline subtraction can result in the signal sometime being negative. These negative values create problems when the logarithm is taken of these negative values. The logarithm operation is used to convert intensity values to attenuation values by taking the logarithm of the measured intensity normalized to a calibration scan in the absence of absorptive material in the imaging volume. Various techniques can be used to correct for negative intensity values, but these corrections introduce a bias to the data, resulting in bias artifacts. Current methods for positivity mapping to correct for negative intensity values do not accurately minimize this bias.